Optimal. Leaf size=59 \[ a^5 \log (x)+5 a^4 b x+5 a^3 b^2 x^2+\frac {10}{3} a^2 b^3 x^3+\frac {5}{4} a b^4 x^4+\frac {b^5 x^5}{5} \]
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Rubi [A] time = 0.02, antiderivative size = 59, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {43} \[ 5 a^3 b^2 x^2+\frac {10}{3} a^2 b^3 x^3+5 a^4 b x+a^5 \log (x)+\frac {5}{4} a b^4 x^4+\frac {b^5 x^5}{5} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^5}{x} \, dx &=\int \left (5 a^4 b+\frac {a^5}{x}+10 a^3 b^2 x+10 a^2 b^3 x^2+5 a b^4 x^3+b^5 x^4\right ) \, dx\\ &=5 a^4 b x+5 a^3 b^2 x^2+\frac {10}{3} a^2 b^3 x^3+\frac {5}{4} a b^4 x^4+\frac {b^5 x^5}{5}+a^5 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 59, normalized size = 1.00 \[ a^5 \log (x)+5 a^4 b x+5 a^3 b^2 x^2+\frac {10}{3} a^2 b^3 x^3+\frac {5}{4} a b^4 x^4+\frac {b^5 x^5}{5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 53, normalized size = 0.90 \[ \frac {1}{5} \, b^{5} x^{5} + \frac {5}{4} \, a b^{4} x^{4} + \frac {10}{3} \, a^{2} b^{3} x^{3} + 5 \, a^{3} b^{2} x^{2} + 5 \, a^{4} b x + a^{5} \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.12, size = 54, normalized size = 0.92 \[ \frac {1}{5} \, b^{5} x^{5} + \frac {5}{4} \, a b^{4} x^{4} + \frac {10}{3} \, a^{2} b^{3} x^{3} + 5 \, a^{3} b^{2} x^{2} + 5 \, a^{4} b x + a^{5} \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 54, normalized size = 0.92 \[ \frac {b^{5} x^{5}}{5}+\frac {5 a \,b^{4} x^{4}}{4}+\frac {10 a^{2} b^{3} x^{3}}{3}+5 a^{3} b^{2} x^{2}+a^{5} \ln \relax (x )+5 a^{4} b x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.37, size = 53, normalized size = 0.90 \[ \frac {1}{5} \, b^{5} x^{5} + \frac {5}{4} \, a b^{4} x^{4} + \frac {10}{3} \, a^{2} b^{3} x^{3} + 5 \, a^{3} b^{2} x^{2} + 5 \, a^{4} b x + a^{5} \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 53, normalized size = 0.90 \[ a^5\,\ln \relax (x)+\frac {b^5\,x^5}{5}+\frac {5\,a\,b^4\,x^4}{4}+5\,a^3\,b^2\,x^2+\frac {10\,a^2\,b^3\,x^3}{3}+5\,a^4\,b\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 60, normalized size = 1.02 \[ a^{5} \log {\relax (x )} + 5 a^{4} b x + 5 a^{3} b^{2} x^{2} + \frac {10 a^{2} b^{3} x^{3}}{3} + \frac {5 a b^{4} x^{4}}{4} + \frac {b^{5} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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